U.S. counter-terrorism experts are losing confidence in Russian security for the Winter Olympics in Sochi after recent suicide bombings targeted a major transportation hub many are expected to use to attend the Games, officials told ABC News this week.

While the Olympic venues in Sochi, the Black Sea resort town hosting the international competition, are being locked down by a massive Russian military cordon, outlying areas in which Olympians, their families and spectators will be transiting are unlikely to be anywhere near as safe from violent Islamist extremists in the region, experts warn.

"I think the real vulnerability may not be within the Olympic games themselves but possibly outside this perimeter where you're going to have a lot of soft targets," House Homeland Security Chairman Michael McCaul (R-Tex.) told ABC News on Thursday.

"Soft targets" are hotels, restaurants, malls and transportation that are not fortified, or "hardened," like military or government installations.

Three suicide bombings that left dozens of Russians dead in the streets of Volgograd since October -- including two attacks late last month -- have alarmed U.S. counter-terrorism officials, who say their worries have elevated amid Russian refusals to fully accept offers of American help on securing the Games. Volgograd, once known as Stalingrad, is 600 miles and 21 hours by train from Sochi. Thursday Russian forces conducted a counter-terrorism sweep of the Stavropol Territory close to Sochi after six bodies were discovered in cars that were rigged to explode, though officials have not determined the motive for those murders.

Top American officials overseeing security preparations for the U.S. Olympic Team -- led in Russia by the U.S. State Department's Bureau of Diplomatic Security with support from the FBI, CIA and NSA -- told ABC News that bombings so far outside the Chechen battlespace signals the militants' confidence in striking distant civilian targets for maximum political effect. Their goal: embarrassing Russian President Vladmir Putin.

The cracks in the U.S.-Russia Olympics security relationship became evident after back-to-back suicide bombings Dec. 29 killed commuters inside the main train terminal and on a city bus destroyed by a blast in Volgograd. No group has claimed responsibility for those blasts, but they were suspected as the handiwork of Chechen militant leader Doku Umarov, who is known as an Islamist and "Russian Bin Laden."

"They're increasing their area of operations and that's troubling," said a U.S. counter-terrorism official who has directly scrutinized Russian security preparations for the Olympics. "Their goal is to give Putin a black eye."

In a message of condolence to the Russian people after the bombings, the White House's National Security Council's wording indicated the Russian's haven't embraced Western security cooperation with open arms.

"The U.S. government has offered our full support to the Russian government in security preparations for the Sochi Olympic Games, and we would welcome the opportunity for closer cooperation for the safety of the athletes, spectators, and other participants," the NSC said in a statement on New Year's Eve.

Asked on Thursday if the Russians had more fully embraced U.S. offers of help securing the Games since then, State Department spokeswoman Jen Psaki said contacts are continuing.

"We've had discussions on counter-terrorism cooperation in a number of venues with the Russians," Psaki told reporters. "We welcome any efforts and willingness and openness to cooperate around the Olympics."

FBI Director James Comey told reporters Thursday the Russians are cooperating with the U.S., echoing a statement made previously to ABC News by a spokesperson for the Russian Embassy in Washington, D.C.

Still, an American official, speaking on condition of anonymity, said there "are clearly sensitivities in our relationship with Moscow," even if Olympics security is of "mutual interest."

"The Volgograd bombings underscore the threat and why it makes sense to work hand-in-hand with Russia to ensure the protection of U.S. citizens participating in and attending the Games in Sochi," the official told ABC News.

U.S. intelligence interpreted October's Volgograd bus bombing, carried out by a female suicide bomber and caught on another Russian drivers' dashboard camera, as Umarov following through on his videotaped threat last July, which ordered his followers to do what they can do stop the Olympics.

That the October explosion and the follow-up attacks in late December took place in Volgograd is especially troubling to Georgetown University scholar Christopher Swift, who has studied the resistance against the Russian government in Chechnya and Dagestan and who also has interviewed scores of militants.

"Anybody traveling by ground to the Olympics likely will have to go through Volgograd," Swift told ABC News.

The bombings in the city, which famously held off the Third Reich's advance during World War II when it was known as Stalingrad, mean that for Umarov's followers the Winter Games "are an operational priority and that they have the capability" to strike outside of their traditional area of activity, Swift said.